Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
296 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #30631454 | C2 | semidirect |
| 5. #30631453 | C2 | semidirect |
| 6. #30631453 | C2 | semidirect |
| 7. #342×C251 | C2 | semidirect |
| 11. #22548671 | C4 | semidirect |
| 15. C22⋊C4×D251 | C4 | semidirect |
| 118. C251 | #1828 | semidirect |
| 126. #342 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632160 | 2 |
| C2×#22548629 | 2 |
| #30631454 | 2 |
| #30631453 | 2 |
| #342×C251 | 2 |
| #1828 | 251 |